How to practice Martial Arts?
Choose. It all depends on what you want. Do you want to learn at a calm, slow pace until you get the moves right? Or do you want to advance fast, training as though you are in a combat situation and quickly learning how to correct mistakes. The choice depends on you, your age, your physical condition, etc.
Decide on the school. Which school? There are many factors that go into choosing a school to train in. Search on this site for "how to choose a martial arts school" for information. This is very important, as the style and master you decide on greatly affects how you learn.
Be in somewhat decent shape. You don't have to work out before hand, since martial arts isn't about strength. But endurance is key. You will learn to fight 1 on 1 or 10 on 1 eventually, so the faster you can move for a long period of time the better you will perform.
Understand the tradition. The original purpose of martial arts was so people could defend themselves against multiple attackers, even to the death. Much has changed, and there are many people today who misjudge the purpose of martial arts. The true purpose is to train to stay alive against many people who are trying to kill you.
Understand the role of your sensei. Your master is your friend, your motivation, and your worst enemy (if he is good). He/she should push you beyond your believed capabilities training you to never give up during a fight. Ask him/her for help, but try to figure things out for yourself first. Understand you're not the only one there, others have come for the same reason so don't keep the instructor to yourself. Don't be a loner either, or you'll never learn. Realize his job and yours before you join a school.
Respect your dojo. There are no games here. You don't fool around, especially while your sensei is speaking. Respect your dojo as much as you respect your fellow students. Always show up early for lessons.
Understand the motivations of other students. Your purpose for being at a dojo might not be the same as some peoples'. If there are kids, they want to be power rangers or show off their moves to friends. If there are adults, the younger ones are arrogant and wild. The older adults just there to learn. You will meet all types. If the sensei is a good one, he will quickly dismiss any student who is out of order and continue the lesson. Show no attention to anyone who acts for others and not himself.
Trust your yuki. Eventually, you will be assigned a yuki. While only for the one lesson, this person is your trusted partner. You must show each other great, mutual respect for you will be fighting him. This is the person you practice your moves on, or spar against, and they you. Depending on the style, learn what attacks to hold back power on so you don't injure this person. When practicing techniques, do them slow until you gain the right control. Help your yuki learn as well as you do. On the other hand, have no sympathy for this person. When you spar, do it violently with control. Don't go easy on them but don't hit them hard. In a nutshell: attack fast and aggressively, but with controlled power. You are there to learn to defeat people like this, not to play around.
Develop the right mindset. You will do aerobics, you will sweat, you will be tired, and you will get hurt. But do not stop. If you practice right, you will hurt someone or get hurt yourself. Don't take it personally. If you are sparring and get injured, take a few breaths and don't resume with the fury you will have. You will feel like swinging wildly and acting aggressively to keep them at a distance, but do not do this. The concept behind martial arts is staying calm while staying alive. If you are not calm, your yuki will get mad or worse, your sensei will. If you injure your opponent, don't apologize, just don't do it again. Wait for them to signal ready and resume sparring.
Practice. Practice every technique you are shown until it becomes second nature, and then some. Think beyond what you are shown and question your sensei about it. Figure out what else could work for that situation. Strip down anything you don't like. Unless you are having a test on the subject, it's always best to keep the simple ideas rather than the 21-step takedown.